Studies of combined forecasts have typically constrained the combining weights to sum to one and have not included a constant term in the combination. In a recent paper, Granger and Ramanathan (1984) have argued in favour of an unrestricted linear combination, including a constant term. This paper shows that for the purpose of prediction it may make sense to impose restrictions on the combining model because of potential increases in forecasting efficiency. Empirical results show that small gains in forecasting efficiency can be obtained by restricting the linear combination of GNP forecasts from four econometric models.
KEY WORDS Combining forecasts Regression Linear constraints
Forecast efficiency and bias
In a seminal paper, Bates and Granger (1969) showed that a linear combination of forecasts can outperform the individual forecasts. Subsequent studies on combined forecasts have focused on simple averages of the individual forecasts (e.g. Makridakis and Winkler, 1983) or weighted averages where the weights are constrained to sum to one (Newbold and Granger, 1974; Nelson, 1972; Dickinson, 1975). Many published studies have shown that simple averages or averages that take into account the relative precisions of the forecasts can perform better than the individual forecasts. However, combination techniques that attempt to make use of sample information about the interdependence of forecasts have performed poorly in general, and many schemes have been proposed for improving the performance of such combinations. Granger and Newbold (1977, chap. 8) provide an overview. In a recent article Granger and Ramanathan (1984) propose including a constant term and not restricting the weights to sum to one in the linear combination of forecasts. They state that the Lcommon practice of obtaining a weighted average of alternative forecasts should . . . be abandoned in favour of an unrestricted linear combination including a constant term' (emphasis in original). Essentially, Granger and Ramanathan suggest that we perform a simple OLS regression with the actual value as the dependent variable and the forecast values as the independent variables.
The purposes of this paper are (1) to examine analytically the implications of Granger's and Ramanathan's proposal and (2) to subject their claim to an empirical test. The message of the 0277-6693/86/01003